What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to

Which statement.........

Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

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The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.

The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.

An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.

The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2

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Answer:

Slope=-3.333/2.000=-1.667

X-intercept= -13/5 = -2.60000

Y-intercept= -13/3 = 14.33333

On solving the provided question, we can say that the equation of the expression is given by y = 6x + 50

Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.

From the table we can see that if the equation be

y = mx + c

for x = 0 y = 50

c = 50

again from x = 1 and y = 56

m = 6

So the equation of the expression is given by y = 6x + 50

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Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .

The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,

we have to find the after how many hours there will be only 50 mg of medication left ;

we need to substitute f(t) as 50 ;

we get ;

⇒ [tex]50 = 200e^{-0.4t}[/tex] ;

⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;

⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]

On solving further ,

we get ;

⇒ [tex]t=3.4657..[/tex] hours ;

So , t≈ 3.47 hours .

Therefore , After 3.47 hours there will be 50 mg of medication left .

The given question is incomplete , the complete  question is

Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?

(a) 4.37 hours

(b) 7.47 hours

(c) 3.47 hours

(d) 3.74 hours

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Answer:

  1.033×10⁴

Step-by-step explanation:

You want the quotient 40.79÷0.003949​ using log tables.

The log of a quotient is the difference of logs:

  log(a/b) = log(a) -log(b)

It can work well to start by writing the numbers in scientific notation:

  log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106

  log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965

Then the log of the quotient is ...

  log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141

The antilog of this number will be ...

  antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴

With our 4-digit log tables, 4 significant figures is the best we can expect.

The quotient is about 1.033×10⁴.

__

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The positive value of the distance between the two objects

is  [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.

The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]

[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].

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The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.

Several rules for exponents are

Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!

Dividing the first number by the second using the quotient rule, it would be

= (1.782 × 10⁹) / (8.1 × 10⁶)

= (1.782/8.1) × (10⁹/10⁶)

= 0.22 × 10⁹⁻⁶

= 0.22 × 10³

In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

So,

0.22 × 10³ = 2.2 × 10²

Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².

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A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.

As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.

There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.

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No, 12, 20, and 16 do not form a Pythagorean triple. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a^2 + b^2 = c^2.

To determine if 12, 20, and 16 form a Pythagorean triple, we can substitute each number into the equation and solve for c.

Start by substituting 12 for a, 20 for b, and 16 for c:

12^2 + 20^2 = 16^2

144 + 400 = 256

544 ≠ 256

Since 544 does not equal 256, the numbers do not form a Pythagorean triple. We can also verify this by calculating the square of c to see if it is equal to the sum of the squares of a and b.

Start by substituting 12 for a, 20 for b, and 16 for c:

a^2 + b^2 = c^2

12^2 + 20^2 = c^2

144 + 400 = c^2

544 = c^2

Taking the square root of both sides:

√544 = √c^2

23.2 ≠ c

Since 23.2 does not equal c, the numbers do not form a Pythagorean triple.

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The equation of the line is 3x + y - 11 = 0.

The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:

y = -3 x + 10

Therefore, the slope of the line is m= -3

Now since the equation of the line with slope m passing through a point

(x₁ ,y₁) is y-y₁ = m(x-x₁)

Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:

y - 8 = -3(x - 1)

y - 8 = -3x +3

3x + y - 11 = 0

Hence, the equation of the line is 3x + y - 11 = 0.

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The sum of first 20 terms of the AP will be -206.25

As in AP, let us assume that the "a" be the first term and 'd' be the common difference.

So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.

So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)

And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)

Now subtracting (ii) from (i),

We will get,

4d = 2(1/2)

=>4d = 2.5

=>d = (2.5/4) = 0.625

Now putting value of "d" in (i)

We will get,

a+(18*0.625) = -5

a=-5-11.25 = -16.25

We have, the formula for finding the sum of terms:

Sum of terms can be determined by using formula:

Sum = (n/2) × [2a + (n-1)d]

Here, n = 20, a = -16.25, d = 0.625

We will get sum of first 20 terms as:

[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]

10[-32.5+11.875]

=10(-20.625) =-206.25

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The Complete is showing the length of the fence and the cost.

Length of fencing  4  6      7    9  10

Cost:                       36 54  63 81  90

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Length of fencing  4  6  7  x  10

Cost:                       36 y z 81 w

Now, Using proportion

4/ 36 = 6/y

4y = 36(6)

y = 54

and, 4/36 = 7/z

4z = 36 (7)

z = 63

and, 4/36 = x /81

x = 9

and, 4/36 = 10/w

360 = 4w

w= 90

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In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.  

Diagonal of a rhombus bisects the angles of the rhombus at the vertex.

So as m∠MNL is 120°,

∠MNO = ∠LNO = 120/2 = 60°

The diagonals intersect each other at a 90 degree angle, therefore

m∠MON = 90°

Considering ΔMNO, right angled at O.

cos(∠MNO) = NO/ MN

cos(60) = NO/ 8

NO = 0.5×8 = 4

NP = NO + OP

NP = 2NO

NP = 2×4

NP = 8 in

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Answer:

Step-by-step explanation:

In ratio and proportion , when we compare two ratios or we can say two fractions then they are said to be equivalent when both of them are same.

The reason to choose problem B over A is simple -  it is more relatable to them.

Problem A involves dinosaurs, which may be more interesting to students than the abstract concept of creating an area with rope. Additionally, the use of feet as a unit of measurement in Problem A may be more familiar to students than inches.

Finding a number that represents the quantity of anything is called measurement. An accepted quantity that is used to represent a physical quantity is called a measurement unit. Let's learn about some of the standard units used to measure physical quantities.

The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.

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The roots of the equation 2x² - 3x - 5 = 0 are 5/2 and -1.

The quadratic formula is a formula that can be used to find the solutions (or roots) of a quadratic equation. For a quadratic equation written in the form ax² + bx + c = 0, where a, b, and c are constants, the quadratic formula is given by:

x = (-b ± √(b²- 4ac))/(2a)

Where x is the solution, a, b, and c are the coefficients of the equation.

Plug in the coefficients of the equation 2x² - 3x - 5 = 0 to the quadratic formula to find the roots.

x = (-b ± √(b²- 4ac))/(2a)

x = (3 ± √((-3)²- 4(2)(-5)))/(2)(2)

x = (3 ± 7)/4

x = 5/2   ;   x = -1

Hence, the roots of the equation are 5/2 and -1.

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The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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Answer: Constructions A, B, and D can be accomplished with paper folding.

Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.

Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.

Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.

Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.

Step-by-step explanation:

The following constructions can be accomplished with paper folding -

Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -

Given is to find which of the following constructions can be accomplished with paper folding.

The following constructions can be accomplished with paper folding -

Therefore, the following constructions can be accomplished with paper folding -

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The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.

As given in the question,

Let 'W' is the random variable represents the number of walleye.

'P(W)' represents its probability

The values are given as follow:

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Mean of the walleye 'W' is given by :

= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)

= ( 0 ×  0.09 )  + ( 1 × 0.42 ) + ( 2 × 0.49 )

= 0 + 0.42 + 0.98

= 1.4

Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.

The above question is incomplete , the complete question is :

Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets

if she catches 2 fish.

W      :        0                        1                       2

P(W)  :        0.09                0.42                  0.49

Calculate the mean of W.

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The person who has the most number 1 in UK is Elvis Presley. He has a total of 21 number 1 which is the highest in history.

The UK Singles Chart is a chart which numbers musician on the basis of their songs and their sales and streams it  was created in 1969. The records and statistics listed here, however, date back to 1952 .

The song which charted the charts was Old Town Road which was recently remixed and launched by Lil Nas X.

Elvis Aaron Presley or more commonly known as Elvis, was an American singer and actor. He dubbed the "King of Rock and Roll", and is now regarded as one of the most significant cultural figures of the 20th century.

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Ericka’s mistake is in ''Step 2.''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation.

Now,

Since, Ericka was solving an exponential equation.

Clearly, The equation is,

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

Step 1;

⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴

⇒ 5 ⁹ˣ⁺⁶ = 5 ² ⁽³ˣ ⁻ ²⁴⁾

Step 2;

⇒ 9x + 6 = 2 (3x - 24)

So, Ericka’s mistake is in Step 2.

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The value of f(4) - g(-5) if function  f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x) = 3 / 2x + 2 and g(x) = 2x² - 3

Calculate the value of f(4) and g(-5) as shown below,

f(4) = 3 / 2 × 4 + 2

f(4) = 12 / 2 + 2

f(4) = 6 + 2

f(4) = 8

g(-5) = 2 × (-5)² - 3

g(-5) = 2 × 25 - 3

g(-5) = 50 - 3

g(-5) = 47

Now, calculate the value of f(4) - g(-5) as shown below,

f(4) - g(-5) = 8 - 47

f(4) - g(-5) = -39

Thus, the value of f(4) - g(-5) is -39.

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Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

A system of equations for this problem can be written as:

x + y = 10 (1) equation for the total number of herbs planted

0.50x + 0.25y = 3 (2) equation for the total cost of the herbs

Where x is the number of basil plants and y is the number of mint plants.

Using substitution, we can solve the system of equations.

Solving equation (1) for x, we get x = 10 - y

Substituting this into equation (2) we get:

0.50(10 - y) + 0.25y = 3

5 - 0.50y + 0.25y = 3

5 = 0.75y + 3

0.75y = -2

y = -2/0.75 = -8/3

So, Eden planted -8/3 mint plants, which doesn't make sense, as a fraction of plant are not possible. This implies that either the number of plants or the amount spent are incorrect or something is missing in the problem description.

As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.

assessing the mathematical function that represents the algorithm's growth rate when input is added;

200 = 10k, where k is the proportionality constant.

k = 200/10

k = 20

The function that represents the number of iterations is as a result:

I = input size; n = 20i; represents the number of iterations.

As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

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I would choose to draw a sample of 20 marbles in order to make a more accurate prediction.

In general, it is generally better to draw a larger sample if you are trying to make a prediction. This is because a larger sample will provide more information and will therefore lead to a more accurate prediction.

For example, imagine that you are trying to predict the proportion of red marbles in a bag based on the samples that you draw. If you draw a sample of 10 marbles, there is a good chance that the proportion of red marbles in your sample will be different from the true proportion of red marbles in the bag.

However, if you draw a sample of 20 marbles, the proportion of red marbles in your sample will be more likely to be closer to the true proportion of red marbles in the bag.

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